
Here, the coefficients \(c_{\Delta _\alpha }^* = \eta _{\Delta _\alpha }/\eta _\chi \)  quantify the three pre-existing flavored \(B\!-\!L\)  asymmetries generated during \(N_{2,3}\)  leptogenesis, while \(c_\perp ^*\)  specifically measures the pre-existing asymmetry along the flavor direction in \(e\)  – \(\mu \)  flavor space that is immune to \(N_1\)  wash-in leptogenesis.
Given our convention chosen above, \(c_\perp ^* = \eta _{\Delta _\mu }/\eta _\chi \) , while more generally, one may give the protected flavor direction a new name and write \(c_\perp ^* = \eta _{\Delta _\perp }/\eta _\chi \)  (see also the notation and conventions in Ref. [1]}).
The explicit value of \(c_\perp ^*\)  is model-dependent but calculable.
Given a specification of all parameters in the RHN sector, one is able to use standard results for thermal leptogenesis or the formalism for wash-in leptogenesis developed here and in Ref. [1]} to compute the coefficient \(c_\perp ^*\) .
